Probability and statistics question

[juniordant]

In a lottery, 6 numbers are drawn out of 45. You hit a jackpot if you guess all 6
numbers correctly, and get $400 if you guess 5 numbers out of 6. What are the
probabilities of each of those events?

 

[Dr.Peterson]

In a lottery, 6 numbers are drawn out of 45. You hit a jackpot if you guess all 6
numbers correctly, and get $400 if you guess 5 numbers out of 6. What are the
probabilities of each of those events?

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There are several quite different ways to solve problems like these, so it will be helpful to see at least what method you are learning. One way will start with these questions: how many ways are there to draw 6 numbers? How many ways are there for those numbers to match all of your choices?